Catrakilis kicked four penalties and a conversion with a 100 percent success rate to help Province to victory, while the Lions were left to rue costly misses.
The Johannesburg-based visitors missed five convertible penalties as they proved unable to turn a dominant performance into victory.
Flyhalf Marnitz Boshoff's four misses proved costly, including one on the stroke of fulltime that could have tied the match and sent it into extra time.
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Catrakilis slotted his first two penalty attempts, while Boshoff went wide with his opening two efforts, before a rare first-half attack saw Western Province centre Jaco Taute go over for a first try and a 13-0 lead at the break.
The Lions cut the deficit after halftime with a Boshoff penalty. Jaco van der Walt then dived over in the corner and Boshoff's conversion, followed soon after by another penalty success, levelled the scores at 13-13.
But then the ever-accurate Catrakilis added two more penalties to put Province 19-13 up going into the final 10 minutes.
A Lions onslaught in the closing stages forced a penalty and winger Ruan Combrinck, pressed into kicking duties, reduced the deficit with just five minutes to play.
The hosts conceded another penalty right on fulltime, after illegally collapsing a maul, but Boshoff pushed the kick wide to spark wild celebrations from the home crowd.
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